Course content

Linear and nonlinear state-space modelling applied to relevant modern electrical engineering examples—including but not limited to power converters, electrical machines, wind turbines, etc.

Equilibrium analysis and direct equilibrium control. Introduction to industry-standard linear control structures: open loop equilibrium control, P, PI, PID control, full-state feedback and cascaded lead/lag compensators.

Visualizing time-domain responses in Matlab and Simulink. Linearization of nonlinear models. Modal transformation and eigenvalue analysis (including parametric sweeps). Frequency domain analysis via Laplace transformation, transfer functions, block diagrams, and performance specifications of second-order systems. Frequency response, bode-plots, relative stability (gain margin and phase margin). The root locus method. Design of cascaded compensators using Bode plots and the Root Locus Method. Controllability and observability and integrated design of full-state feedback control with observers. Introduction to optimal control.

Learning outcome

Knowledge:

After completing the course, the student will have acquired knowledge about mathematical modelling of at least one of the most electric industry-relevant dynamical power devices (converters, machines, turbines, etc.) in the time- and frequency-domain.

The student will have gained understanding on the main differences between linear and nonlinear (electrical) systems, how to characterize their equilibrium, and control them by means of state-feedback, P, PI, PID controllers and cascaded lead/lag compensators .

The student will become familiar with the most relevant modelling formalisms used in modern electrical engineering practice such as state-space modelling, transfer functions and block diagrams. In addition, the student will learn how to linearize nonlinear systems, and assess their small-signal stability by means of an eigenvalue analysis.

Moreover, the student will be able to derive transfer functions from their linearized system, analyze their stability by means of their pole locations, represent them by means of block diagrams and obtain closed-loop transfer when cascaded with a compensator. Furthermore, the student will learn basic techniques to approximate resulting closed-loop transfer functions to simpler second-order ones (without zeros or extra poles), such as to enforced a desired dynamical performance in terms of e.g.: percent overshoot, peak/rise-time, etc. They will also get familiar with the final value theorem as a useful tool to guarantee desired steady-state errors for different inputs (step, ramp, etc.).

In addition, the student will learn about how to perform a frequency response with their system and sketch approximated Bode plots. They will gain understanding of relative stability concepts such as phase and gain margins, will be able to identify these directly in the Bode plot, as well as improve them by adding a lead or lag compensator. The student will familiarize themselves with the Root Locus methos, as a powerful tool for designing and tuning linear controllers.

Finally, the students will gain understanding on the all-important controllability and observability concepts, widely used in control engineering and learn how to check if their systems are controllable and observable. They will also learn to design integrated full-state feedback and observers, and get an introduction to optimal control.

Skills:

Know how to model and analyze stability of dynamical electrical systems relevant in modern electric power engineering, set their control objectives and design and synthetize stabilizing and performant controllers.

General competence:

Be able to carry out small development projects independently and contribute actively in the classroom. Increased report writing skills as well as communication skills. Increased Simulation (Simulink) skills as well as numerical computation skills (Matlab).

Learning methods and activities

Theorethical lectures once every two weeks supported by offline in-depth and mathematically rigorous video tutorials combined with workshops two or three sessions a week where students work on weekly assignments under the supervision of the lecturer and scientific/student assistants—which allows for one-on-one interaction between students and the teaching staff. Assignments will be a mixture between theoretical developments, computations in Matlab, as well as time-domain simulations in Simulink on relevant applications for modern electric power engineering.

Recommended previous knowledge

Introduction to Analog and Digital Electronics (TTT4203), Calculus 3 (TMA4110) and Circuits and Power System Analysis (ELDI2003) Calculus 1 (TMA4100) and 2 (TMA4105).

Course materials

Book: Richard Dorf, Robert Bishop: Modern Control Systems.